1. Given that the position of a particle is defined in terms of time by the equation below, where x is in meters and t is in seconds, determine: x = t 4t3 +t2 3t2 + 4 t3 (a) the average velocity of the particle from t = 1.0 s to t = 3.0 s, (Ans: vape = 16 m/s) (b) the instantaneous velocity of the particle at t = 2.5 s, (Ans: v, = 20.52 m/s) (c) the average acceleration of the particle from t = 2.0 s to t = 3.0 s, and (Ans: aave = 8.42 m/s?) (d) the t at which the instantaneous acceleration of the particle is 8.10 m/s. (Ans: t = 3.91 s)

1. Given that the position of a particle is defined in terms of time by the equation below, where x is in meters and t is in seconds, determine: x = t 4t3 +t2 3t2 + 4 t3 (a) the average velocity of the particle from t = 1.0 s to t = 3.0 s, (Ans: vape = 16 m/s) (b) the instantaneous velocity of the particle at t = 2.5 s, (Ans: v, = 20.52 m/s) (c) the average acceleration of the particle from t = 2.0 s to t = 3.0 s, and (Ans: aave = 8.42 m/s?) (d) the t at which the instantaneous acceleration of the particle is 8.10 m/s. (Ans: t = 3.91 s)

Name: 1. Given that the position of a particle is defined in terms of time
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Description: 1. Given that the position of a particle is defined in terms of time by the equation below,where x is in meters and t is in seconds, determine:x =t4t3 +t2 3t2+ 4t3(a) the average velocity of the particle from t = 1.0 s to t = 3.0 s, (Ans: vape = 16

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 6P: The position of a particle moving along the x axis varies in time according to the expression x =...

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The position of a particle moving along the x axis varies in time according to the expression x = 3t2, where x is in meters and t is in seconds. Evaluate its position (a) at t = 3.00 s and (b) at 3.00 s + t. (c) Evaluate the limit of x/t as t approaches zero to find the velocity at t = 3.00 s.
3. Given that the position of particle is defined in terms of time by the equation below, where x is in meters, and t is in seconds, determine: 3t2 + 4 t3 X = a) the average velocity of the particle from t = 1.0s to t = 3.0s (Ans. 16 m/s) b) the instantaneous velocity of the particle at t = 2.5 s (Ans. 20.52 m/s) c) the average acceleration of the particle fromt = 2.0s to t = 3.0s (Ans. 8.42 m/s²) d) the time t which the instantaneous acceleration of the particle is 8.10 m/s? (Ans. 3.91 s)
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